Question

4. При якому значенні m вектори a(m; 5) і b (8; -20) а) колінеарні; б) перпендикулярні

Answer 1

Ответ:

а) колінеарні

Объяснение:

отак повинно бути

Answer 2

a(m; 5) and b(8; -20) are collinear when their direction vectors are parallel, which means the ratio of their corresponding components is constant.

To check for collinearity, we can compare the ratios of the corresponding components of the vectors:

a(m; 5) = (m; 5) b(8; -20) = (8; -20)

The ratio of the corresponding x-components is:

m/8

The ratio of the corresponding y-components is:

5/(-20) = -1/4

If the two vectors are collinear, these ratios should be equal. Therefore, we can set up an equation:

m/8 = -1/4

To find the value of m, we can cross-multiply and solve for m:

4m = -8 m = -8/4 m = -2

Thus, when m = -2, the vectors a(-2; 5) and b(8; -20) are collinear.

To determine when the two vectors are perpendicular, we can use the dot product. Two vectors are perpendicular if and only if their dot product is zero.

The dot product of a(m; 5) and b(8; -20) is:

(m * 8) + (5 * -20) = 8m - 100

To find the value of m for which the vectors are perpendicular, we can set the dot product equal to zero and solve for m:

8m - 100 = 0 8m = 100 m = 100/8 m = 12.5

Therefore, when m = 12.5, the vectors a(12.5; 5) and b(8; -20) are perpendicular.